By # 3913, we have $$\tan 9^\circ + \tan 81^\circ=\frac{2}{\sin 18^\circ}=\frac{2\times 4}{\sqrt{5}-1}=2\times(\sqrt{5}+1)$$

and \begin{align*} \tan 27^\circ + \tan 63^\circ &= \frac{2}{\sin 54^\circ}=\frac{2}{\cos 36^\circ}=\frac{2}{1-2\sin^2 18^\circ}\\ &=\frac{2}{1-2\times(\frac{\sqrt{5}-1}{4})^2}=2\times(\sqrt{5}-1) \end{align*} Therefore, the original expression equals $$2\times(\sqrt{5}+1)-2\times(\sqrt{5}-1)=\boxed{4}$$